Question: Solve for $x$ and $y$ using elimination. ${-x-6y = -16}$ ${x+5y = 15}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $-y = -1$ $\dfrac{-y}{{-1}} = \dfrac{-1}{{-1}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {-x-6y = -16}\thinspace$ to find $x$ ${-x - 6}{(1)}{= -16}$ $-x-6 = -16$ $-x-6{+6} = -16{+6}$ $-x = -10$ $\dfrac{-x}{{-1}} = \dfrac{-10}{{-1}}$ ${x = 10}$ You can also plug ${y = 1}$ into $\thinspace {x+5y = 15}\thinspace$ and get the same answer for $x$ : ${x + 5}{(1)}{= 15}$ ${x = 10}$